Question

The freezer compartment in a conventional refrigerator can be modeled as a rectangular cavity 0.3 m high and 0.25 m wide with a depth of 0.5 m. Determine the thickness of styrofoam insulation (k = 0.30 W/m⋅K) needed to limit the heat loss to 400 W if the inner and outer surface temperatures are −10 and 33°C, respectively.

Answer 1

Thickness of Styrofoam insulation is 0.02741 m.

Step-by-step explanation:

Given that,

Height = 0.25 m

Depth = 0.5 m

Power = 400 W

Temperature = 33°C

We need to calculate the area of Styrofoam

Using formula of area

`A=2(lb+bh+hl)`

Put the value into the formula

`A=2(0.3*0.5+0.25*0.5+0.5*0.3)`

`A=0.85\ m^2`

Inner surface temperature of freezer

`T_(i)=-10°C=263\ K`

Outer surface temperature of freezer

`T_(o)=33+273=306\ K`

We need to calculate the thickness of Styrofoam insulation

Using Fourier law,

`q=(kA)/(L)(T_(o)-T_(i))`

`L=(kA)/(q)(T_(o)-T_(i))`

Put the value into the formula

`L=(0.30*0.85)/(400)(306-263)`

`L=0.02741\ m`

Hence, Thickness of Styrofoam insulation is 0.02741 m.